Digital/analog arithmetic with continuous-valued residues

Residue number system (RNS) representations, which allow fast addition and multiplication, have found niche applications in signal processing. These representations are based on integer-valued residue ¿digits¿ with respect to integer moduli. We introduce RNS representations with continuous or analog digits, and study their dynamic range, accuracy, and optimal choice of the moduli. Like positional number systems with continuous digits, our representations offer advantages in robustness and fault tolerance. As an interesting application, we point to recent findings in computational neuroscience that attribute a rat´s uncanny ability to return to a home position, even in the absence of visual clues, to a related hex-grid-based residue representation of its position.